Under the product reference bases, the entanglement of assistance \(E_a\)  is just the coherence of assistance \(C_a\)  for all pure states as well as for Schmidt correlated states \(\rho _{mc}=\sum _{ij} \rho _{ij}|ii\rangle \langle jj|\)  [1]}, \(E_a(\rho _{mc})=C_a(\rho _{mc})\) . The similar results also hold true for the entanglement of convex roof \(E_c\)  and the coherence of convex roof \(C_c\) . The correspondence not only bridges coherence theory and entanglement theory, but also generalizes many results in entanglement theory to coherence theory.
